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Acoustic Gas Thermometry
Roberto M. Gavioso
1st June 2017
28th Meeting of the Consultative Committee for Thermometry (CCT)
CCT/17-29
outline Acoustic Gas Thermometry
hystorical development
• development of theory: Laplace was finally right
• wide ranging applications of acoustic gas thermometry ...
• ... including primary temperature standards
ongoing work and future perspectives
• extending the temperature range of primary acoustic thermometers
• alternatives for dissemination: simplification of primary methods
• practical acoustic thermometers
results
• determinations of the molar gas constant R and the
Boltzmann constant k
• determinations of T-T90
milestones along a successful road
• theory and practice of a sphere
• son et lumiere: advantages of the new SI
1627 - Francis Bacon
gedanken experiment To try exactly the time wherein sound is propagated
[..] let a man stand in a steeple, with a candle, veiled; and let
another man stand a mile off: then let the person in the steeple
strike a bell and at the same instant withdraw the veil; the other, at
a distance, may measure the time between the light seen and the
sound heard, for light is propagated instantaneously*
*Or what comes very near thereto, for in the space of seven or
eight minutes it is thought by some to travel from the sun to the
earth.
transient method 1635 - Pierre Gassendi
478 m/s
Marin Mersenne 1636
448 m/s
Cogitata Physico
Mathematica
steady-state method
Benedicam Dominum, Benedicam Dominum Benedicam Dominum
1656 - Viviani, Borelli
360 m/s
1708 - Derham, Flansted, Halley
348 m/s
at 20 °C, 1 atm, 50% relative humidity
speed of sound in air
344 m/s
Sylva Sylvarum 1627
2 1
p
S V
cpc
c
1687 Newton
1816 Laplace
2 1=
T
pc
2 4
pc
1727 Euler
Newton (isothermal)
T = const
Laplace (adiabatic)
S = const
dQ = 0
wavelength mean free pathl
1S
p
1T
p
21 S
S
cp
1
Sp
1S
S
V
V p
0 50 100 150 200 250 300 350 4000
200
400
600
800
1000
1200
1400
1600
Tc
isothermal speed of sound
liquid water
water vapor
sp
ee
d o
f so
un
d / m
s-1
Temperature / °C
adiabatic speed of sound
liquid water
water vapor
21L s
S
pc
K
2
T
S
pc
G
longitudinal waves
shear waves
bulk modulus
shear modulus
versatility of Laplace equation
1965 - 1975 up to 20000 K He: 300 K - 2000 K, 2 MPa 1962
sonic anemometry (& thermometry)
2 MT u
R
sonic temperature
w' T '
sonic kinematic heat flux
turbulent heat flux
sonic anemometers are sensors that are able to estimate wind speed vector
by measuring the influence of local wind speed on the transmission of
ultrasound signals between pairs of emitters and receivers that configure
acoustic paths. This estimation is normally assigned to the geometric center
of acoustic path midpoints
sonic anemometers are used to evaluate the turbulent heat flux from the sonic
kinematic heat flux (or “temperature flux”), i.e. the covariance of the vertical wind
velocity w and the sonic temperature T the vertical wind velocity w and the
speed of sound c being simultaneously measured by the anemometer, and the
speed of sound being then corrected for the effect of the crosswind
Acoustic Thermometry of Ocean Climate (ATOC) precision 50 ms – accuracy 0.1 s ≈ 0.05 K
3.3 kW at 57 Hz 206 dB
1994
2015
abstract: measuring temperature changes of the deep oceans, important for determining the oceanic heat content and its impact on the Earth’s
climate evolution, is typically done using free-drifting profiling oceanographic floats with limited global coverage. Acoustic thermometry provides
an alternative and complementary remote sensing methodology for monitoring fine temperature variations of the deep ocean over long distances
between a few underwater sources and receivers. We demonstrate a simpler, totally passive (i.e., without deploying any active sources)
modality for acoustic thermometry of the deep oceans (for depths of ~ 500–1500 m), using only ambient noise recorded by two existing
hydroacoustic stations of the International Monitoring System. We suggest that passive acoustic thermometry could improve global monitoring of
deep-ocean temperature variations through implementation using a global network of hydrophone arrays
(A) Locations of the two hydroacoustic stations (red
dots) near Ascension and Wake Islands.. (B)
Zoomed-in schematic of the hydrophone array
configurations for the Ascension and Wake Island
sites, which both have a similar layout. Each
hydroacoustic station consists of a northern and
southern triangle array of three hydrophones (or
triad), with each triangle side equal to approximately
2 km. The distance L between triad centers is equal
to 126 km and 132 km for the Ascension and Wake
Island stations, respectively.
(C) Noise cross-correlation waveforms, averaged
over three different years, obtained between all 9
pairwise combinations of the elements of the north
and south triads for the Wake Island. (D) Same as
C, but for Ascension Island. The beams shown by
dashed lines in A are centered on the lines joining
the centers of the south and north triads of each
hydroacoustic station (yellow line) and which
intersect the Polar regions where potential ice noise
sources contributing to the coherent arrivals shown
in C-D are located (18b).
ideal gas assumptions:
• the molecules of the gas are indistinguishable, small, hard spheres
• collisions are elastic and motion is frictionless (no energy loss)
• Newton's laws apply
• average distance between molecules is much larger than molecular size
• the molecules constantly move in random directions with a distribution of speeds
• there are no attractive or repulsive forces between the molecules
22
02
rmsvu
0 5 3 monoatomic gas 2 2
0 0 0 0
1
3rms
S
p kT RTu T v
m M
squared mean
molecular speed molar mass molecular mass
1873
Alfred Marshall Mayer
Koenig flame
manometer (1862) Wheatstone revolving mirror
(1834)
ambient to 1000 °C
kTmvrms
2
3
2
1 2 mean
kinetic energy p RT Mideal gas
equation of state
1979 273.16 K
8.4 ppmru R
1965
2 K ÷ 20 K
repeatabilty 3 mK
[..] We felt that experimental determination of
isotherms from measurements of the speed of
sound in helium gas as a function of pressure was
a promising approach. The concept of deriving
values of absolute temperature from speed-of-
sound measurements is not of recent origin. Lord
Rayleigh recognized the possibility of such an
experiment in 1878 in observations on a
communication from A. M. Mayer [..].
[..] Since gas thermometry is the method which has
been most widely used for achieving temperature
values that approach values on the thermodynamic
scale, the technique was given serious
consideration. But precise gas thermometry is a very
painstaking undertaking, especially at low
temperatures, where certain difficulties are
intensifled [..]
thermal viscous shell ducts
2 N
N
au f f f f f
z
-23 -1 -1
A 1.380 651 3 0.000 002 5 10 J mol Kk R N (1.8 ppm)
1988
1979 - 1988
bulk thermal viscous ducts Ng g g g g
22
2 sound
0 20
B B Blight
frequencyenergy mass velocity masstemperature lim
frequencypc
k k k
ac
ac
2 ,, ,
a p Tu p T f p T
z
mw
mw
2 ,, ,
a p Tc p T f p T
z
ac mw
acmw
, ,
, ,
u p T f p T z
c p T zf p T
1986
1999
217 K to 303 K
2
20TPW TPW
,lim
,p
u p TT
T u p T
2000
90 K to 300 K
2003
303 K, 430 K, 505 K
2004 234 K to 380 K
18
8 1 10f
f
precision
improved frequency measurement
6 < 1 10f
f
accuracy
2004
2006 77 K to 273 K
2007
271 K to 552 K
2008 -2011 iMERA- Plus Research Project
Determination of the Boltzmann constant
for the redefinition of the kelvin
coordinator J. Fischer
on-lathe interferometry
23 1
2 2rmskT mv
composition
(including isotopes)
of test gases
liquid He cold trap
heated getter
mass spectrometry
6 3 4 60.03 10 He He 1 10 60.25 10M M
helium argon
2010
Ar 0 1 ppmru M .
2015
Ar 0 6 ppmru M .
june 2017 Ar 0 4 ppmru M .
The new kelvin 31 August 2015 Page 23 of 48
Thermodynamics vs. ITS
0.1
1
10
100
1000
10000
100000
1900 1920 1940 1960 1980 2000 2020
Rel
ativ
e er
ror
or r
epro
duci
bili
ty, p
pm
Year
Boltzmann's constant
Temperature scales
Metrologia Boltzmann Special Issue 2015, R. White and J. Fischer Figure 1: Relative uncertainty in the value of Boltzmann’s constant. Also shown is the relative reproducibility of the practical temperature scales, in the vicinity of 100 C.
determinations of k with AGT and other methods 2017 (yesterday)
AGT with cylindrical cavities
Johnson noise thermometry (JNT)
60 59 10ru k .
60 70 10ru k .
61 95 10ru k . 62 10ru k
67 5 10ru k .
25 50 75 100
-7.5
-5.0
-2.5
0.0
2.5
WG4 u(WG4)
PTB - DCGT 2015 - (C1 - He)
PTB - DCGT 2015 - (C1, C2 - He, Ne)
LNE-CNAM - AGT 2015
LNE-CNAM - AGT 2006
UCL - AGT 2000
NRC - RIGT 2017
(T-T
90)
/ m
K
Temperature / K
100 150 200 250 300 350 400-10
-8
-6
-4
-2
0
2
4
6
8
10
NPL - AGT 2015
NPL - AGT 2016
INRiM - AGT 2016
VNIIFTRI - AGT 2017
NIM - AGT 2017
LNE - AGT 2015
(T-T
90)
/ m
K
Temperature / K
2012 - 2017 AGT data
2012 - 2015 EMRP Research Project
Implementing the new kelvin - InK
coordinator G. Machin
coordinator G. Machin
2016 -2019 EMRP Research Project
Implementing the new kelvin 2 - InK2
T-T90 by Acoustic Gas Thermometry (AGT) between 430 K and 933 K
Inconel pressure
vessel 1 MPa @
1000 K
Benefits
• 2-stage pulse-tube cryostat no LHe
• 2 thermal shields and 2 vacuum chambers
• minimum temperature < 4 K
• same calorimeter for T and T90 realization
• houses a larger number of CSPRTs
• provides good stability especially
in ranges 30 K – 77 K and
150 K – 234 K
Risks and drawbacks
• vibrations could affect measurements
• complex design, needed long realization
time
coordinator G. Machin
2016 -2019 EMRP Research Project
Implementing the new kelvin 2 - InK2
T-T90 by Acoustic Gas Thermometry between 5 K and 200 K
extending the temperature range of primary thermometers
The cold valve The prototype sphere
The Cryogenic Current Comparator
Amplification and its shield
AGT at T < 4 K
8 cm
16 cm
22 c
m
termination of acoustic and microwave waveguides
• material: copper; shape: triaxial ellipsoid; interrnal radius: 4 cm; interrnal volume: 260
cm3; thick wall to minimize shell coupling; the cavity is designed to be vacuum- and
pressure tight
• excitation of acoustic and microwave resonances by waveguides
• embedded thermometer wells for cSPRTs and long-stem SPRTs
• working gas: helium (calculable properties) purity maintained by a getter
• temperature range of initial tests: 230 K to 430 K;
• aimed accuracy: ± 5 ppm
2 2 2
0 1 2 , , ... u p T u p T A T p A T p
measured calculable for He
alternatives for dissemination: simplification of primary methods
assembled
calibration zone with
Peltiers
Microphone and Loudspeaker in stabilised zone